Optimal Dual g-Frames and Error Analysis for 2-Erasures

Authors

  • Asghar Rahimi University of MARAGHEH
  • S. Sadeghi Dijaz University of MARAGHEH
  • E. Alizadeh Department of Mathematics, Mara. C., Islamic Azad University Marand, Iran

Abstract

In this paper, we investigate the behavior of dual g-frames in
Hilbert spaces under the assumption of 2-erasures. During data trans-
mission, some coecients may be lost in communication networks. We
explicitly formulate the error operator associated with the loss of two
indices and provide rigorous upper bounds for the reconstruction error
norm and show how the use of non-canonical dual g-frames introduces
perturbation operators in the reconstruction process. Furthermore, we
demonstrate how non-canonical dual g-frames introduce specific pertur-
bation operators, concluding with a numerical example to illustrate the
theoretical results. Also, we prove novel theorems addressing the opti-
mal reconstruction problem, demonstrating the exact conditions under
which the reconstruction error is minimized when utilizing specific op-
timal dual g-frames. Finally, a numerical example is provided to verify
the theoretical results.

Published

2026-09-16

Issue

Vol. 21 (2027)

Section

No. 1

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